AFAIK installing packages via HM does not automatically give you the right includes. Either set $NIX_CFLAGS_COMPILE (and potentially $NIX_LDFLAGS) manually (or pass -I argument to the compiler or use a development shell while declaring your inputs (protobuf) there. This will then automatically populate the aforementioned env variables automagically.

Sounds like you have installed protobuf via Home Manager or nix-profile and/or are using the system’s compiler instead of one installed through nix?

All compilers in the nix package store are wrapped in custom shell scripts that injects the needed paths the compilers are looking for in FHS directories. In case of gcc glibc and libcxx, as well as $NIX_COMPILER_FLAGS (name from the top if my head) which is populated by nix depending on what is installed. For example, if you would use a nix development shell (classic or flake based) and install protobuf there, the correct include paths the wrapped compiler needs would be contained in this variable.

Have a look at https://nixos.wiki/wiki/C which answers a few questions and look at the wrapper code of gcc (in the gcc package) which points to gcc-unwrapped.